# formula
pi=0
N=100
for k in range(N):
    pi+=1/pow(16,k)\
        *(4/(8*k+1)-2/(8*k+4)-1/(8*k+5)-1/(8*k+6))
print(pi)

# MonteCarlo
from random import random
DARTS=1000**2
hits=0.0
for i in range(1,DARTS+1):
    x,y=random(),random()
    dist=pow(x**2+y**2,0.5)
    if dist<=1.0:
        hits+=1
pi=4*(hits/DARTS)
